City boss Roberto Mancini is desperate to bolster his attack during the summer and has placed an experienced winger on his shopping list as plots to conquer the Champions League next season.
Robben fits the bill but with Etihad Stadium chiefs ordering the Italian to cut costs he is looking at alternative methods to fund a move for the Holland international.
One of those involves Bosnian international Dzeko who has been deemed surplus to requirements by the Premier League champions after spending a frustrating campaign on the bench.
The 26-year-old has failed to reproduce the form he displayed during his time at Wolfsburg and could now be set for a return to the Bundesliga just 18-months after leaving to join City for £27 million.
Mancini was hoping to sell Dzeko to Bayern in a straight cash £32 million deal to boost his transfer coffers as he chases Robben and Arenal striker Robin Van Persie.
German newspaper Bild has suggested that Munich would open to City’s proposal of an exchange that see them pay a minimal fee for Dzeko whilst new signing Xherdan Shaqiri has already been lined up as a replacement for Robben.
The 28-year-old only signed a new three-year deal at the Allianz Arena in May but his future at the club is uncertain after a bust-up with team-mate Franck Ribery.
He was also unhappy after being booed by his own supporters following his penalty miss in the Champions League final against Chelsea although his father Hans Robben instead he will be remaining at Bayern.
However he has a history of using deceitful tactics to orchestrate moves for his son having stated back in 2004 that Robben wouldn’t be joining Chelsea before signing for them later that year.